Q. If p and q vary inversely and p is 9 when q is 5 , determine q when p is equal to 3 .Answer:
Given relationship and constant: Given that p and q vary inversely, we can write the relationship as p=qk, where k is the constant of variation.
Find constant of variation: We know that p is 9 when q is 5. We can use these values to find the constant of variation k. Substitute p with 9 and q with 5 into the equation p=qk. 90
Write inverse variation equation: To find k, multiply both sides of the equation by 5.9×5=k45=k
Substitute values and solve: Now that we have the constant of variation k, we can write the inverse variation equation as p=q45.
Find value of q: We want to find q when p is equal to 3. Substitute p with 3 into the equation p=q45.3=q45
Find value of q: We want to find q when p is equal to 3. Substitute p with 3 into the equation p=q45.3=q45To solve for q, multiply both sides of the equation by q and then divide by 3.3q=45q=345q=15
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